Linear receivers for solar collectors

ABSTRACT

Described herein are linear receivers for use in concentrating solar collection applications. For example, linear receivers incorporating a volume displacement element within an internal volume of a linear solar radiation absorbing element are provided. The volume displacement element provides, for example, enhanced heat transfer characteristics between the absorber element and the heat transfer fluid, efficiency improvements associated with maintaining a position of the linear receiver at an optimal location for absorbing concentrated solar radiation and/or the ability to recover the linear receiver from a freeze event. Also provided are methods for making a linear receiver, methods for collecting concentrated solar radiation, methods for recovering a linear receiver from a freeze event, methods for improving overall receiver efficiency, such as by reducing bowing/sagging of the receiver element, and methods for reducing a circumferential temperature distribution of the absorber element.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority from U.S. Provisional Patent Application No. 61/924,034, filed Jan. 6, 2014, which is hereby incorporated by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with governmental support under award No. DE-FC36-08GO18034 awarded by the Department of Energy. The government has certain rights in the invention.

TECHNICAL FIELD

This invention is in the field of solar thermal power generation. This invention relates generally to a linear receiver for a concentrating solar collection system.

BACKGROUND

Solar receivers for linear concentrating solar thermal collection systems generally include an absorbing receiver tube in which a heat transfer fluid flows, with the absorbing receiver tube housed within a transparent glass envelope to protect the absorbing receiver tube and reduce heat loss from the absorbing receiver tube. Various techniques have been employed to increase the efficiency of solar receivers for linear concentrating solar thermal power generation systems. For example, a vacuum can be introduced between the glass envelope and receiver tube to minimize conductive heat losses. Additionally, an antireflection coating can be placed on the glass envelope to maximize transmission of solar radiation to the absorbing receiver tube. Further, an absorbing coating on the receiver tube itself can maximize light absorption and reduce radiative losses.

Other techniques for improving efficiency include using solar receivers comprising a transparent glass receiver tube and employing an optical-absorber inside the receiver tube to facilitate the conversion of solar radiation to thermal energy. For example, U.S. Patent Application Publication No. US 2013/0319501 describes including an optically-absorbing additive directly within the heat transfer fluid. Similarly, U.S. Patent Application Publication No. US 2009/0293866 describes placing an absorbing insert with internal flowpaths for the heat transfer fluid within the receiver tube.

Other techniques have been applied to increase the efficiency of solar receivers, such as by implementing an insulating material around a conventional receiver tube or by placing an insulating material or dividers within the region between the glass envelope and the coated receiver tube to minimize convective losses, as described, for example, in U.S. Patent Application Publication No. US 2013/0276775.

For vertically aligned receiver tubes, such as in solar power tower configurations, the flow of the heat transfer fluid presents challenges, as the heat transfer fluid must ultimately be returned to the ground, necessitating both upward and downward flow channels. U.S. Patent Application Publication No. US 2013/0220310 overcomes this obstacle by providing a solar receiver having concentric tube modules, where the heat transfer fluid flows in an upward direction in an outer toroidal channel as it absorbs heat from the walls of the receiver tube, and is returned to the ground in an inner channel.

SUMMARY

The present invention provides, for example, linear receivers for concentrating solar collectors with various enhancements. Aspects of the invention involve incorporating a volume displacement element within an internal volume of a linear solar radiation absorbing element. Use of a volume displacement element provides a number of benefits. For example, such a volume displacement element reduces the available volume for flowing a primary heat transfer fluid within the receiver, resulting in an overall higher flow velocity and providing enhanced heat transfer characteristics, which in turn enables a more uniform circumferential temperature distribution of the absorbing element. In addition, flow turbulators are incorporated into various aspects and embodiments of the invention to further enhance heat transfer between the absorber element walls and the heat transfer fluid.

The volume displacement element also provides for reduction of bowing and sagging of the absorbing element, for example, by reducing the stresses associated with a non-uniform circumferential temperature distribution and, for example, by reducing the weight of the heat transfer fluid within the absorbing element. These reductions in bowing and sagging, for example, can also provide an improvement in efficiency, by maintaining a position of the linear receiver at an optimal location for absorbing concentrated solar radiation, such as at a focus of a parabolic trough reflector. Use of a volume displacement element also provides, for example, for linear receivers capable of recovering from a freeze event, such as by providing a location for internally heating a solid heat transfer fluid and by providing for the ability to accommodate an increase in the heat transfer fluid's volume upon melting, such as by use of a volume displacement element with a collapsible geometry.

The present invention also provides, for example, methods for collecting concentrated solar radiation, methods for recovering a linear receiver from a freeze event, methods for improving overall receiver efficiency, such as by reducing sagging and/or bowing of a linear receiver, by reducing a circumferential temperature distribution of the linear receiver and by improving the efficiency of heat transfer from the walls of the linear receiver to the heat transfer fluid inside the receiver. In various embodiments, these techniques are achieved by providing a linear receiver, such as described herein, or by retrofitting an existing linear receiver to incorporate a volume displacement element or other aspects of the invention.

In a first aspect, the invention provides linear receivers for concentrating solar collectors. A specific receiver embodiment of this aspect comprises: a linear solar radiation absorbing element extending along a first length and comprising a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; a linear volume displacement element positioned within the linear solar radiation absorbing element and extending along at least a portion of the first length of the linear solar radiation absorbing element, where the first internal volume includes a second volume occupied by the linear volume displacement element and a third volume not occupied by the linear volume displacement element, where the second volume occupies a percentage of the first internal volume greater than 15%; and a first heat transfer fluid provided within the third volume, where the first heat transfer fluid flows at a first flow rate within the linear solar radiation absorbing element but does not flow within the second volume. In an exemplary embodiment, the second volume occupies a percentage of the first internal volume selected from the range of 15% to 90%. In various embodiments, the second volume occupies a percentage of the first internal volume greater than 20%, 25%, 30%, 35% or 40% or selected from the range of 20% to 80%, 30% to 70% or 40% to 60%.

In certain embodiments, use of the linear volume displacement element provides for improved heat transfer between the linear solar radiation receiving element and the first heat transfer fluid, for example an improved heat transfer as compared with a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the same first flow rate but not including the linear volume displacement element. Such an improved rate of heat transfer optionally provides for a more uniform circumferential temperature distribution of the linear solar radiation absorbing element thereby resulting in minimized bowing of the linear solar radiation receiving element away from the optimal location for receiving concentrated solar radiation. Such bowing can occur where there is a large circumferential temperature distribution throughout the linear solar radiation absorbing element. For example, hotter portions of the linear solar radiation absorbing element undergo more thermal expansion than cooler portions of the linear solar radiation absorbing element, resulting in stresses that form bowed or sagged regions of the linear solar radiation absorbing element.

In various embodiments, for example, the maximum circumferential temperature difference results in reduced bowing, reduced stresses and/or reduced strain along the linear receiver as compared with a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the first flow rate but not including the linear volume displacement element. In a specific embodiment, the first flow rate of the first heat transfer fluid provides for a heat transfer rate or heat flux between the linear solar radiation absorbing element and the first heat transfer fluid sufficient to maintain a maximum circumferential temperature difference of the linear solar radiation absorbing element to achieve a target amount of bowing, stress and/or strain in the linear solar radiation absorbing element. In one embodiment, the maximum circumferential temperature difference is less than 100° C.

Without being limited by any theory, it is believed that, in embodiments, a target circumferential temperature distribution achieved by a specific heat transfer rate and/or heat flux results from an increase in convective heat transfer between the linear solar radiation absorbing element and the first heat transfer fluid as compared to a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the first flow rate but not including the linear volume displacement element. In some embodiments, the flux incident on a collector aperture of a linear concentrating solar thermal collection system, such as a reflective surface of a parabolic trough, ranges from 100 W/m² to 1100 W/m². Optionally, the flux incident on the linear solar radiation absorbing element can be as high as or larger than 80000 W/m². In embodiments, however, a flux incident on the linear solar radiation absorbing element is a function of the size of the solar receiver field, the incident angle of the sun, the concentration ratio of the collection system, the collection efficiency of the system, etc.

In embodiments, an increase in convective heat transfer occurs because the first flow rate has an increased linear velocity as compared to a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the first flow rate but not including the linear volume displacement element. For example, in one embodiment, the presence of the linear volume displacement element achieves a percentage increase in linear velocity of the first heat transfer fluid selected from the range of 115% to 1000%. As the mass or volumetric flow rate is optionally the same whether or not the linear receiver includes the linear volume displacement element, including the linear volume displacement element will result in a higher linear flow rate as a portion of the volume of the linear solar radiation receiving element is occupied by the linear volume displacement element. In embodiments, for example, the linear volume displacement element occupies between 15% and 90% of the first internal volume of the linear solar radiation absorbing element. One of skill in the art will appreciate that it is straightforward to convert between volumetric flow, mass flow and linear flow using fluid properties and geometries of the cross sectional areas through which a fluid flows. Further details are provided in Example 5 below.

Various volume displacement elements are useful with the devices and methods of the invention. For example, in one embodiment, the linear volume displacement element comprises glass, ceramic, stainless steel, Inconel, a metal alloy comprising greater than 50% nickel, steel, metal or any combination of these. In an exemplary embodiment, the linear volume displacement element comprises an electrically conductive material. In one embodiment, for example, the linear volume displacement element extends along a percentage of the first length selected from the range of 25% to 100% or from the range of 50% to 100%. Useful linear volume displacement elements include both solid structures and hollow structures. In various embodiments, the linear volume displacement element has a cross-sectional shape selected from the group consisting of a circle, an oval, an ellipse, a rectangle and a square. In an exemplary embodiment, the linear volume displacement element is positioned concentrically within the linear solar radiation absorbing element.

In some embodiments, the linear volume displacement element comprises two or more linear volume displacement elements. Optionally, the linear volume displacement element comprises two or more linear volume displacement elements having their ends joined by welds. Optionally, one or more linear volume displacement elements comprise an end cap. In certain embodiments, two or more linear volume displacement elements are positioned in electrical communication with one another by an electrical bridge.

Advantageously, embodiments of the invention including the linear volume displacement element provide a reduction in an overall mass of the linear receiver sufficient to reduce sagging, stress and/or strain in the linear solar radiation absorbing element compared with an overall mass of a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the first flow rate but not including the linear volume displacement element. For example, such a reduction in mass, in embodiments, reduces sagging along the linear receiver as compared with a linear receiver comprising the linear solar radiation absorbing element having the first internal volume occupied by the first heat transfer fluid having the first flow rate but not including the linear volume displacement element. Such a reduction in mass is optionally achieved, for example, in embodiments where the linear volume displacement element has an overall density less than a density of the first heat transfer fluid. In certain embodiments, the overall density is a percentage of the density of the first heat transfer fluid. In embodiments, such a reduction in mass is achieved, for example, because the first heat transfer fluid is not flowing within the second volume and/or is not present within the second volume.

In certain embodiments, the linear volume displacement element comprises a second hollow structure, such as cylindrical tube. In embodiments, the second hollow structure has a wall thickness selected from the range of 0.5 to 5 mm. In embodiments, the second hollow structure has a wall thickness that is a percentage of a diameter of the second hollow structure, such as a percentage selected from the range of 1% to 40%. Optionally, linear receivers of this aspect further comprise a second heat transfer fluid provided within the second hollow structure. For example, useful fluids for the second heat transfer fluid include liquids or gases, such as heat transfer fluids comprising water, steam, oil or molten salts or a heated gas or a heated liquid. Including a second heat transfer fluid is useful, for example, to recover from a freeze event of the first heat transfer fluid. For example, in one embodiment, a first melting temperature of the first heat transfer fluid is greater than a second melting temperature of the second heat transfer fluid. In an exemplary embodiment, the first heat transfer fluid is a solid and the second heat transfer fluid has a temperature greater than a melting temperature of the first heat transfer fluid.

Optionally, linear receivers of this aspect include those embodiments where the linear volume displacement element comprises a collapsible geometry. Use of a linear volume displacement element comprising a collapsible geometry are beneficial, for example, for recovering from a freeze event where the first heat transfer fluid experiences a reduction in volume upon freezing and/or an expansion in volume upon melting. In embodiments, for example, melting of the first heat transfer fluid results in an increase in volume occupied by the first heat transfer fluid with the volume of the linear volume displacement element reducing upon the increase in volume occupied by the first heat transfer fluid, thereby preventing breaking, fracturing, deforming or damaging the linear solar radiation absorbing element upon melting of the first heat transfer fluid.

For example, in one embodiment, the linear volume displacement element collapses from a volume greater than the second volume as a temperature of at least a portion of the first heat transfer fluid is increased from a first temperature below a melting temperature of the first heat transfer fluid to a second temperature above the melting temperature of the first heat transfer fluid. In another embodiment, for example, the linear volume displacement element expands from the second volume to a greater volume as a temperature of at least a portion of the first heat transfer fluid is decreased from a first temperature above a melting temperature of the first heat transfer fluid to a second temperature below the melting temperature of the first heat transfer fluid.

Optionally, collapsible geometries are provided by a variety of linear volume displacement elements. For example, in embodiments, the linear volume displacement element comprises one or more flexible regions and/or one or more convoluted regions. Such collapsible geometries, optionally, provide the linear volume displacement element with the ability to deform.

In embodiments, a variety of solar radiation absorbing elements, also referred to herein as absorber tubes, are useful with the devices and methods of the invention. In one embodiment, for example, the linear solar radiation absorbing element comprises a cylindrical tube. In various embodiments, for example, the linear solar radiation absorbing element has a cross-sectional shape selected from the group consisting of a circle, an oval, an ellipse, a rectangle and a square. In certain embodiments, use of a specific cross-sectional shaped radiation absorbing element can provide further enhancements to a solar collection system, such as by reducing the mass of the heat transfer fluid inside and by providing an optimal absorbing area for a specific concentrating system. For example, in one embodiment, a radiation absorbing element having an elliptical cross-sectional shape is used in a linear Fresnel system.

In exemplary embodiments, the linear solar radiation absorbing element of linear receivers of the invention has an average temperature greater than 300° C., greater than 400° C., greater than 500° C., greater than 600° C. or less than 600° C., for example when the receiver is exposed to concentrated solar radiation. In exemplary embodiments, the linear solar radiation absorbing element of linear receivers of the invention maintains an average temperature greater than a melting temperature of the first heat transfer fluid, for example when the receiver is not exposed to concentrated solar radiation. In one embodiment, the linear solar radiation absorbing element of linear receivers of the invention has an average temperature greater than or equal to an ambient temperature when the receiver is not exposed to concentrated solar radiation.

Useful linear solar radiation absorbing elements include, but are not limited to those comprising stainless steel. In a specific embodiment, a linear solar radiation absorbing element comprises an absorbing layer or coating provided on the external surface, such as an absorbing layer adapted to absorb all, a portion of or a majority of solar electromagnetic radiation incident on the absorbing layer.

In certain embodiments, linear receivers of the invention further comprise one or more turbulators positioned within the third volume. Use of turbulators within the third volume, such as exposed to the first heat transfer fluid, advantageously increase turbulence within the first heat transfer fluid and optionally increase a heat transfer rate or heat flux between the linear solar radiation absorbing element and the first heat transfer fluid. For example, in embodiments, the one or more turbulators enhance turbulence within a flow of the first heat transfer fluid as compared with a flow of the first heat transfer fluid without the one or more turbulators. In one embodiment, for example, the one or more turbulators comprise one or more cylindrical pins or cylindrical support legs positioned with a cylindrical axis perpendicular to a flow direction of the first heat transfer fluid and/or one or more helical objects positioned with a helical axis parallel to a flow direction of the first heat transfer fluid.

A variety of heat transfer fluids are useful with the devices and methods of the invention. For example, useful heat transfer fluids, such as for the first heat transfer fluid, include, but are not limited to, those comprising oil, synthetic oil, a salt, a salt mixture, salt peter, sodium nitrate, potassium nitrate, calcium nitrate, supercritical CO₂, water, steam, aqueous mixtures, such as including a glycol or other additives which decrease corrosion or depress freezing point, or any combination of these. In some embodiments, the first heat transfer fluid has a melting temperature selected from the range of 100° C. to 300° C.

In certain embodiments, linear receivers of the invention further comprise a hollow glass structure positioned such that the linear solar radiation absorbing element is located within the hollow glass structure. Glass outer structures, also referred to herein as glass envelopes, are useful for protecting the linear solar radiation absorbing element and for minimizing conductive heat losses from the linear solar radiation absorbing element, such as by containing an insulating material or vacuum around at least portions of the linear solar radiation absorbing element.

In one embodiment, for example, the hollow glass structure comprises a cylindrical tube. Optionally, the hollow glass structure has a cross-sectional shape selected from the group consisting of a circle, an oval, an ellipse, a rectangle and a square. In exemplary embodiments, the hollow glass structure is transparent to at least a portion of the terrestrial solar spectrum thereby permitting solar radiation to pass through the hollow glass structure and be absorbed by the linear solar radiation absorbing element. Optionally, the linear solar radiation absorbing element is positioned concentrically within the hollow glass structure. Certain embodiments also further comprise one or more support elements to fix the linear solar radiation absorbing element within the hollow glass structure.

In various embodiments, linear receivers of the invention comprise one or more support elements to fix the linear volume displacement element within the linear solar radiation absorbing element. For example, useful support elements include, but are not limited to, 5-pointed springs and/or support legs, such as cylindrical support legs.

In embodiments, the linear receivers described herein are useful in concentrating solar collectors, such as concentrating solar collectors comprising a reflective parabolic trough solar collector and/or a reflective linear Fresnel solar collector. In exemplary embodiments, the reflective parabolic trough solar collector and/or a reflective linear Fresnel solar collector is positioned such that reflected solar radiation is directed onto the linear receiver.

In other aspects, the present invention provides methods, such as methods of using the linear receivers described above. In various embodiments, the invention provides methods of collecting concentrated solar radiation, such as methods in which a maximum circumferential temperature difference of the linear solar radiation absorbing element is maintained within a specific range to achieve a target amount of bowing, stress and/or strain within the linear solar radiation absorbing element. For example, in one embodiment, the maximum circumferential temperature difference is maintained below 100° C. In some embodiments, however, such a maximum temperature difference could be exceeded briefly without the receiver undergoing damage.

An exemplary method embodiment of this aspect comprises the steps of: providing any of the linear receivers described above; exposing the linear solar radiation absorbing element to concentrated solar radiation, where the first flow rate of the first heat transfer fluid is sufficient to maintain a maximum circumferential temperature difference of the linear solar radiation absorbing element within a specific range to achieve a target amount of bowing, stress and/or strain within the linear solar radiation absorbing element.

Another exemplary method embodiment of this aspect comprises steps of: providing a linear solar radiation absorbing element extending along a first length, wherein the linear solar radiation absorbing element comprises a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; providing a linear volume displacement element within the linear solar radiation absorbing element and extending along at least a portion of the first length of the linear solar radiation absorbing element, wherein the first internal volume includes a second volume occupied by the linear volume displacement element and a third volume not occupied by the linear volume displacement element and wherein the second volume occupies a percentage of the first internal volume greater than 15%; flowing a first heat transfer fluid within the third volume of the linear solar radiation absorbing element, wherein the first heat transfer fluid flows at a first flow rate within the linear solar radiation absorbing element and does not flow within the second volume; and exposing the linear solar radiation absorbing element to concentrated solar radiation, wherein the first flow rate is sufficient to maintain a maximum circumferential temperature difference of the linear solar radiation within a specific range to achieve a target amount of bowing, stress and/or strain within the linear solar radiation absorbing element.

Other exemplary method embodiments of this aspect comprise methods of reducing bowing or sagging of a linear solar radiation absorbing element of a concentrating solar collector. For example, a specific method embodiment comprises the steps of: providing the concentrating solar collector comprising a linear solar radiation absorbing element extending along a first length and a first heat transfer fluid positioned within the linear solar radiation absorbing element and flowing at a first flow rate, wherein the linear solar radiation absorbing element comprises a hollow structure having a first internal volume occupied by the first heat transfer fluid and an external surface for absorbing concentrated or reflected solar radiation; providing a linear volume displacement element within the linear solar radiation absorbing element and extending along at least a portion of the first length of the linear solar radiation absorbing element such that the first internal volume comprises a second volume occupied by the linear volume displacement element and a third volume not occupied by the linear volume displacement element, wherein the second volume occupies a percentage of the first internal volume greater than 15%; and reestablishing the first flow rate of the first heat transfer fluid within the linear solar radiation absorbing element, wherein the first heat transfer fluid does not flow within the second volume and wherein the first flow rate is sufficient to maintain a maximum circumferential temperature difference of the linear solar radiation absorbing element within a specific range when the linear receiver is absorbing concentrated solar electromagnetic radiation, thereby reducing bowing of the linear solar radiation absorbing element.

In embodiments of the above described methods, the first flow rate establishes a rate of convective heat transfer between the linear solar radiation absorbing element and the first heat transfer fluid sufficient to maintain the maximum circumferential temperature difference within a specific range to achieve a target amount of bowing, stress and/or strain within the linear solar radiation absorbing element. In certain embodiments, a target circumferential temperature distribution provides reduced bowing along the linear receiver as compared to a bowing that occurs when the maximum circumferential temperature difference of the linear solar radiation absorbing element is greater than the target circumferential temperature difference, for example greater than 100° C.

In various embodiments, the invention provides methods of collecting concentrated solar radiation, such as methods in which a sagging of the linear solar radiation absorbing element is reduced and/or minimized. An exemplary method embodiment of this aspect comprises the steps of: providing any of the linear receivers described herein, wherein the linear volume displacement element has an overall density less than a density of the first heat transfer fluid; and exposing the linear solar radiation absorbing element to concentrated solar radiation.

Another exemplary method embodiment of this aspect comprises the steps of: providing a concentrating solar collector comprising a linear solar radiation absorbing element extending along a first length and a first heat transfer fluid positioned within the linear solar radiation absorbing element and flowing at a first flow rate, wherein the linear solar radiation absorbing element comprises a hollow structure having a first internal volume occupied by the first heat transfer fluid and an external surface for absorbing incident or reflected solar radiation and wherein the linear solar radiation absorbing element and the first heat transfer fluid within the linear solar radiation absorbing element together have a first mass; providing a linear volume displacement element within the linear solar radiation absorbing element and extending along at least a portion of the first length of the linear solar radiation absorbing element such that the first internal volume comprises a second volume occupied by the linear volume displacement element and a third volume not occupied by the linear volume displacement element, wherein the second volume occupies a percentage of the first internal volume greater than 15%; and reestablishing the first flow rate of the first heat transfer fluid within the linear solar radiation absorbing element, wherein the first heat transfer fluid does not flow within the second volume; wherein the linear solar radiation absorbing element, the linear volume displacement element and the first heat transfer fluid within the third volume together have a second mass that is a percentage of the first mass, thereby reducing sagging of the linear solar radiation absorbing element.

For certain embodiments of the above described methods the concentrating solar collector comprises a plurality of support structures distributed along a length of the linear solar radiation absorbing element for supporting the linear solar radiation absorbing element and the method further comprises a step of removing one or more of the plurality of support structures.

In various embodiments, the invention provides methods of recovering from a freeze event in a concentrating solar collector, such as methods in which the first heat transfer fluid is melted. An exemplary method embodiment of this aspect comprises the steps of: providing any of the linear receivers described herein; cooling the first heat transfer fluid to a first temperature below a melting temperature of the first heat transfer fluid and wherein the linear volume displacement element comprises a second hollow structure and a second heat transfer fluid provided within the second hollow structure; and heating the second heat transfer fluid to a second temperature above the melting temperature of the first heat transfer fluid, wherein heat from the second heat transfer fluid is transferred to the first heat transfer fluid, thereby melting at least a portion of the first heat transfer fluid.

Another exemplary method embodiment of this aspect comprises the steps of: providing any of the linear receivers described herein; cooling the first heat transfer fluid to a first temperature below a melting temperature of the first heat transfer fluid; and heating the linear volume displacement element by passing an electric current along a length of the linear volume displacement element or along a length of the linear solar radiation absorbing element, such as to generate heat by resistive heating, wherein heat from the linear volume displacement element or the linear solar radiation absorbing element is transferred to the first heat transfer fluid, thereby melting at least a portion of the first heat transfer fluid.

Optionally, in various embodiments of the methods described above, the linear volume displacement element comprises a collapsible geometry. For example, in specific embodiments, melting of the first heat transfer fluid results in an increase in a volume occupied by the first heat transfer fluid and wherein the second volume reduces upon the increase in the volume occupied by the first heat transfer fluid, thereby preventing breaking, fracturing, deforming or damaging of the linear solar radiation absorbing element upon the melting of the first heat transfer fluid.

Other exemplary method embodiments of this aspect comprise methods of making concentrating solar collectors. In a specific embodiment, a method of making a concentrating solar collector comprises the steps of: providing any of the linear receivers described herein; and positioning the linear receiver at a location to receive concentrated solar radiation from one or more reflective surfaces.

In another specific embodiment, a method of making a concentrating solar collector comprises the steps of: providing a linear solar radiation absorbing element extending along a first length, wherein the linear solar radiation absorbing element comprises a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; providing a linear volume displacement element within the linear solar radiation absorbing element and extending along at least a portion of the first length of the linear solar radiation absorbing element, wherein the first internal volume includes a second volume occupied by the linear volume displacement element and a third volume not occupied by the linear volume displacement element and wherein the second volume occupies a percentage of the first internal volume greater than 15%; flowing a first heat transfer fluid at a first flow rate within the third volume and between an internal surface of the linear solar radiation absorbing element and the linear volume displacement element, wherein the first heat transfer fluid does not flow within the second volume; and positioning the linear receiver at a location to receive concentrated solar radiation from one or more reflective surfaces.

For various embodiments, the one or more reflective surfaces optionally comprise one or more parabolic trough mirrors or one or more mirrors of a linear Fresnel solar collector. In a specific embodiment, the one or more reflective surfaces comprise one or more parabolic trough mirrors and the linear receiver is positioned at a focus of the one or more parabolic trough mirrors.

Without wishing to be bound by any particular theory, there can be discussion herein of beliefs or understandings of underlying principles relating to the invention. It is recognized that regardless of the ultimate correctness of any mechanistic explanation or hypothesis, an embodiment of the invention can nonetheless be operative and useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a cross-section of an exemplary linear receiver embodiment for a concentrating solar collector.

FIG. 2A depicts a cross-section of a linear receiver for a concentrating solar collector; FIG. 2B depicts a cross-section of an elliptical linear receiver for a concentrating solar collector; FIG. 2C depicts a cross-section of an elliptical linear receiver having an internal tube.

FIG. 3 depicts a cross-section of a linear receiver for a concentrating solar collector.

FIG. 4 depicts a cross-section of a linear receiver having an inner tube.

FIG. 5 depicts a cross-section of a linear receiver having an inner tube supported by a 5-pointed spring.

FIG. 6 depicts a cross-section of a linear receiver having an inner tube supported by a 3-leg spider attached to the inner tube with the 3 rigid legs distributed around the inner tube.

FIG. 7 depicts a schematic illustration of an exemplary receiver embodiment, where the inner tube is concentric with the absorber tube.

FIG. 8 depicts a schematic illustration of components of an exemplary receiver embodiment comprising multiple adjacent inner tubes with ends slid out past the edge of the absorber tube for welding the adjacent inner tubes together.

FIG. 9 depicts a schematic illustration of components of an exemplary receiver embodiment comprising multiple adjacent inner tubes with their ends capped.

FIG. 10 depicts a schematic illustration of components of an exemplary receiver embodiment comprising multiple adjacent inner tubes with their ends capped and with a bridge providing electrical conductivity between the adjacent inner tubes, for example, to pass an electric current for impedance heating.

FIG. 11 depicts a schematic illustration of an absorber tube at the end of the solar collector array fitted with an elbow having a hole so that a straight section of the inner tube can pass through.

FIG. 12 depicts a schematic illustration of components of an exemplary receiver embodiment comprising features (turbulators) to induce turbulent flow of the heat transfer fluid, such as cylindrical pins that are perpendicular to the axis of the inner tube and perpendicular to the flow of the heat transfer fluid.

The reference coordinate systems for a finite element analysis (FEA) of stresses and strains in an absorber for a solar collector are shown in

FIG. 13, which depicts the trough 3-dimensional coordinate system, and

FIG. 14, which depicts the receiver angular position coordinate system.

FIG. 15 provides results illustrating the unit flux distribution on the receiver of a parabolic trough.

FIG. 16 illustrates the differential control volume used in a finite element analysis model.

FIG. 17A provides results showing receiver wall temperature as a function of molten salt flow rate for DNI=1000 W/m², Receiver Outer Diameter=90 mm, Concentration Ratio=80/Tr, and Fluid Temperature=500° C.; FIG. 17B provides results showing receiver wall temperature difference (from wall minimum temperature) as a function of molten salt temperature with DNI=1000 W/m², Receiver Outer Diameter=90 mm, Concentration Ratio=80/Tr, and Flow Rate=8 kg/s.

FIG. 18 provides results showing receiver wall circumferential temperature difference as a function of flow rate for four concentration ratios.

FIG. 19A provides results of a receiver tube FEA model showing the area of peak stress in the receiver tube of a solar collector and FIG. 19B provides results showing maximum stress in a receiver with 90 mm outer diameter, 4.7 m length, and 2.5 mm wall thickness as a function of the difference in temperature between the hot and cold sides of the receiver.

FIG. 20 provides data showing maximum strain in the wall of a receiver as a function of circumferential temperature difference for four receiver wall thicknesses.

FIG. 21 provides data showing maximum allowable receiver wall circumferential temperature difference.

FIG. 22A provides data showing minimum required flow rate to maintain a 500° C. outlet temperature with the given inlet temperature and concentration ratio for a generalized collector loop; FIG. 22B provides data showing the maximum strain in the receivers after 30 years of projected service as a function of inlet temperature, concentration ratio, and an outlet temperature of 500° C. for a generalized collector loop.

FIG. 23A provides data showing required flow rate to maintain a 500° C. outlet temperature with the given inlet temperature and concentration ratio for a generalized solar collector array (SCA); FIG. 23B provides data showing the maximum strain in the receivers after 30 years of projected service as a function of inlet temperature, concentration ratio, and an outlet temperature of 500° C. for a generalized SCA.

DETAILED DESCRIPTION

In general the terms and phrases used herein have their art-recognized meaning, which can be found by reference to standard texts, journal references and contexts known to those skilled in the art. The following definitions are provided to clarify their specific use in the context of the invention.

“Solar radiation absorbing element” refers to a component of a solar collector used for conversion of incident or reflected solar radiation to heat. In embodiments, a solar radiation absorbing element has a surface adapted to absorb solar radiation.

“Volume displacement element” refers to a component of a solar collector which occupies a volume within the solar collector to the exclusion of a primary heat transfer fluid of the solar collector. In embodiments, a volume displacement element contains a secondary heat transfer fluid for transferring heat to or from the primary heat transfer fluid. In embodiments, a volume displacement element comprises a conductive body used to heat a heat transfer fluid surrounding the volume displacement element from within by resistive and/or impedance heating. In embodiments, a volume displacement element has a collapsible geometry such that its volume can accommodate an increase in volume of a heat transfer fluid surrounding the volume displacement element as the heat transfer fluid melts.

“Heat transfer fluid” refers to a component of a solar collector which is used to transfer heat between elements of the solar collector. For example, in embodiments a heat transfer fluid is used to transport heat from a solar radiation absorbing element to elsewhere in the solar collector system, such as to an electrical generator or steam turbine. Useful heat transfer fluids include, but are not limited to, molten salts, oil, liquid water or steam. In embodiments, a molten salt heat transfer fluid can undergo freezing and form a solid body in a solar collector if the temperature of the heat transfer fluid falls below the melting temperature of the heat transfer fluid. In embodiments, a secondary heat transfer fluid is used to melt a frozen primary heat transfer fluid in a solar radiation absorbing element by raising the temperature of the primary heat transfer fluid.

“Linear” refers to a characteristic of an object that extends along a length along a single axis. In one embodiment, the axis of a linear object extends along a straight line. In one embodiment, the axis of a linear object extends along a curved line, such as along an arc.

“Support elements” refer to objects or structures used to support the mass of another object. In embodiments, support elements are used to fix the location of an object in space or within another object. For example, in embodiments, one or more support legs and/or support springs are used to position an object within another object.

“Solar radiation” refers to light generated by the sun. Solar radiation includes incident solar radiation and reflected solar radiation. In some embodiments, the terms “solar radiation” and “terrestrial solar radiation” are used interchangeably and refer to light generated by the sun and transmitted through the earth's atmosphere. Incident solar radiation refers to light received by an object directly from the sun, such as solar radiation transmitted through the earth's atmosphere. Reflected solar radiation refers to solar radiation incident on a reflective object and reflected toward another location or object. For example, in one embodiment, solar radiation incident on a parabolic trough mirror is reflected toward a focus of the mirror and the reflected solar radiation is directed to a receiver or absorber of a solar collector.

“Absorb” and “absorbing” refer to the process of taking up photons of electromagnetic radiation by an object. In certain embodiments, objects are adapted to absorb solar radiation by providing an absorbing layer on the surface of the object.

“Electrical communication” refers to an arrangement of objects such that electric current can flow from one object to another. For example, in one embodiment conductive bodies not in physical contact with one another can be brought into electrical communication with one another by use of an electrical bridge. An “electrical bridge” refers to a conductive object positioned to provide electrical communication between two other objects, such as a conductive object positioned in physical contact with the two other objects.

“Flow rate” refers to a measure of the rate at which a fluid is moving. In embodiments, a flow rate is a mass flow rate, such as a measure of the mass of the fluid flowing past a reference point as a function of time. In embodiments, a flow rate is a volumetric flow rate, such as a measure of the volume of the fluid flowing past a reference point as a function of time. In embodiments, a flow rate is a linear flow rate, such as a measure of the distance traveled by the fluid flowing past a reference point as a function of time.

“Heat transfer” refers to a process of moving thermal energy from a warmer material to a colder material. In embodiments, heat transfer is quantified as a heat transfer rate or a heat flux. In an embodiment, for example, a heat transfer rate refers to the amount of energy transferred between two objects as a function of time. In an embodiment, for example, a heat flux refers to the amount of energy transferred between two objects through a defined area as a function of time.

“Circumferential temperature difference” refers to a difference between two temperatures of an object measured at different points around the circumference or perimeter of the object. In one embodiment, a circumferential temperature difference refers to the temperature difference between two points around the circumference of a cylindrical object. In one embodiment, a circumferential temperature difference refers to the temperature difference between two points around the perimeter of an object having a non-circular cross-section, such as a rectangular cross-section or an elliptical cross-section. In embodiments, the phrase “circumferential temperature distribution” refers to a variation of the temperature of an object around the circumference or perimeter of the object.

“Turbulator” refers to an object placed in a flowing fluid to enhance, introduce or otherwise increase a turbulence of the fluid.

“Concentric” refers to the arrangement of two or more objects such that the objects possess a common center. In one embodiment, two cylindrical tubes are positioned concentrically when one of the tubes is positioned within the other tube such that the centers of the tubes are aligned. As used herein, however, the term concentric can also refer to the arrangement of two or more objects, one or more of which has a non-circular cross section. For example, in an embodiment, a cylindrical tube can be positioned concentrically inside a tube having an elliptical cross-section, such as by having the centers of the cross-sectional areas aligned.

“Concentration ratio” refers to a ratio of a dimension of a solar collector's collection aperture to a dimension of the receiver on which solar radiation is directed from the solar collector. In one embodiment, the term concentration ratio refers to a ratio of a solar collector's aperture width to a diameter of the receiver. In one embodiment, the term concentration ratio refers to a ratio of the area of a solar collector's aperture to a receiving area of the receiver.

The term “overall” is used herein to refer to a collective measurement of a property of a plurality of objects. For example, in one embodiment, an overall mass of an object or device refers to the total mass of the object or device including any of its subcomponents. In a specific embodiment, the overall mass of a linear receiver for a concentrating solar collector includes the mass of a linear solar radiation absorbing element, a mass of a linear volume displacement element and a mass of a heat transfer fluid within the linear solar radiation absorbing element. Similarly, in another exemplary embodiment, an overall density of an object or device refers to the total volume occupied by the object or device including any of its subcomponents divided by the total mass of the object or device including any of its subcomponents.

“Fluid communication” and “flow communication” refer to an arrangement of objects or volumes such that a fluid, for example a liquid, can flow between the objects or volumes.

“Sagging” and “bowing” refer to a displacement of at least a portion of a linear object resulting from a force on the object, stresses within the object and/or strains within the object.

FIG. 1 depicts a cross-section of an exemplary linear receiver embodiment 100 for a concentrating solar collector. In the embodiment shown, the linear receiver 100 comprises an outer glass envelope 110. Optionally, outer glass envelope 110 comprises an outer surface coating, such as an antireflection coating. Outer glass envelope is transparent for at least a portion of the solar terrestrial spectrum such that all or portions of the incident solar terrestrial radiation can pass through outer glass envelope 110. Inside outer glass envelope, receiver tube 130 is positioned to receive incident or reflected solar terrestrial radiation which passes through outer glass envelope 110. In an exemplary embodiment, an insulator or a vacuum 120 is positioned between receiver tube 130 and outer glass envelope 110. Use of insulator or vacuum 120 minimizes conductive and/or convective heat losses from receiver tube 130. In exemplary embodiments, receiver tube 130 comprises an external layer or coating to optimize the absorption of solar terrestrial radiation and conversion to heat energy. Heat transfer fluid 140 is positioned within receiver tube 130 and is used to transport heat from absorbed solar radiation elsewhere for use, such as to an electrical generation system. Also positioned within receiver tube 130 is volume displacement element 150, which occupies a portion of the internal volume of receiver tube 130. In the embodiment shown in FIG. 1, volume displacement element 150 includes internal space 160, which is optionally filled with a second heat transfer fluid or other material; however, heat transfer fluid 140 is not permitted to flow within internal space 160.

Use of volume displacement element 150 provides the linear receiver with a number of advantages. For example, in embodiments, the flow rate of heat transfer fluid 140 is established at a mass or volumetric flow rate similar to or identical to that which would otherwise be used in the absence of volume displacement element 150. Since a portion of the volume of receiver tube 130, however, is occupied by volume displacement element 150, the linear flow rate of heat transfer fluid is higher than the linear flow rate which would otherwise be used in the absence of volume displacement element 150. Advantageously, such an increased linear flow rate will result in improved heat transfer from receiver tube 130 to heat transfer fluid 140 due to an increase in convective heat transfer by way of the increased linear flow rate.

In turn, the improved heat transfer from receiver tube 130 to heat transfer fluid 140 will result in a more uniform circumferential temperature distribution of receiver tube 130. Non-uniform circumferential temperature distributions can occur, for example, in embodiments where only a portion of receiver tube 130 receives focused solar radiation from a reflective structure, such as in a parabolic trough system where primarily the bottom of receiver tube 130 receives focused solar radiation. The resultant non-uniform circumferential temperature distributions can impart stresses that result in bowing of receiver tube 130. These stresses arise from the increased thermal expansion of the hotter portions of receiver tube 130 as compared to the cooler portions of receiver tube 130. By having a more uniform circumferential temperature distribution less bowing of receiver tube 130 will occur, resulting in improved efficiency by maintaining the location of the linear receiver at an optimal location for receiving concentrated solar radiation, such as at the focus of parabolic trough receiver.

Additionally, in some embodiments, the combined mass of the volume displacement element 150 and any contents in internal space 160 is less than an equivalent volume of heat transfer fluid 140, resulting in a reduced mass for the system as compared to a linear receiver lacking volume displacement element 150. Such a reduction in mass will result in less sagging of the receiver tube 130 and improved efficiency by maintaining the location of the linear receiver at an optimal location for receiving concentrated solar radiation, such as at the focus of parabolic trough receiver, as compared to a linear receiver lacking volume displacement element 150 where the sagging will move portions of the receiver tube away from the optimal location for receiving concentrated solar radiation.

Further, in some embodiments, heat transfer fluid 140 may freeze by cooling to a temperature below the melting point. Volume displacement element 150 optionally provides for the ability to heat the frozen heat transfer fluid 140 from within in order to return heat transfer fluid 140 back to a liquid state. Such heating can be provided by passing a second heat transfer fluid having a temperature above the melting point of heat transfer fluid 140 through internal space 160 or by passing an electric current through volume displacement element 150 to generate heat by resistive heating.

Additionally, for some embodiments, volume displacement element 150 is optionally provided with a collapsible geometry. Such a configuration provides advantages for recovering from freeze events, such as described above, as the collapsible geometry of volume displacement element 150 is beneficial for accommodating any increase in volume of frozen heat transfer fluid 140 that occurs upon melting that would otherwise result in fracturing, deforming or damaging of receiver tube 130.

The invention may be further understood by the following non-limiting examples.

Example 1 Elliptical Receiver for Linear Fresnel Collectors

Linear Fresnel collectors can achieve very large apertures without incurring commensurate wind loads. Although this offers several efficiencies, one consequence of a large-aperture linear Fresnel design is that receivers become larger. If the receiver is circular in cross-section, similar to a parabolic trough receiver, then the cross-sectional area of the receiver grows with the square of the increase in receiver diameter. This in turn has several consequences. First, the weight of the receiver and fluid combination grows rapidly, causing receiver sag and the need to include additional structure material. Second, the fluid linear velocity decreases, leading to long fluid transit times, which in turn reduce the responsiveness of the collector field.

A second problem applies to linear Fresnel collectors operating with molten salt as a working fluid. The salt may freeze, requiring freeze recovery. The best freeze recovery strategy is to add heat from the interior of the receiver, since this is where the frozen salt-free surface is expected, due to the receiver freezing from the walls inward. Thawing in the vicinity of this free surface is advantageous because it allows room for the thawing salt to expand, without exerting undue stress on the receiver.

The observations above indicate that it is beneficial to reduce the receiver perimeter and fluid carrying cross-sectional area, as well as to provide a means of central heating for freeze recovery. This example provides embodiments to achieve these beneficial outcomes by means of a linear Fresnel collector which is elliptical in cross-section, and which contains internal elements. These internal elements provide structural stiffness, internal volume displacement, and trace heating capability, either individually or in combination. The embodiments described in this example exploit the pattern of light reflected onto the receiver from a linear Fresnel collector array to provide a receiver with reduced cross-section while still providing a suitable target for light capture.

FIG. 2B shows an example elliptical receiver, shown in comparison to a receiver in FIG. 2A. The elliptical receiver in FIG. 2B maintains the 300 mm dimension in the vertical direction, but has a reduced diameter in the horizontal direction. This characteristic shape is well-matched to the light reflected from a linear Fresnel collector, since light reflected from a mirror under the receiver arrives in a near-vertical direction with a narrow beam spread, while light from a more distant mirror at the collector edge arrives at an angle approaching horizontal, with a wider beam spread. This receiver provides a good optical target for all the mirrors, but reduces both receiver perimeter and cross-sectional area.

Ultimately, reductions in receiver outer dimensions are limited by the minimum optical target size required to efficiently capture reflected light. This places a limit on receiver perimeter reduction. However, cross-sectional area can be further reduced by including an internal tube, as shown in FIG. 2C. This tube displaces additional working fluid, reducing fluid cost, the weight inside the receiver, and fluid transit time. The internal tube also provides an excellent heat trace element, since it can provide a heat source within the tube to recover from a freeze event. This is important, because frozen molten salt needs room to expand while thawing, and the available free surface is likely to be at the interior of the tube after salt freezing starts at the receiver walls and propagates inward. The heat may be provided by either running a hot fluid down the tube, or by electrical means.

FIGS. 2A-2C. Note that the dimensions shown in FIGS. 2A, 2B and 2C are just an example and are not intended to be limiting. The vertical dimensions may change, for example, in response to selected collector aperture size and concentration ratio, and the horizontal dimension may change based on optical performance optimization. Meanwhile, the dimensions of the internal tube may also change, for example, based on overall system cost optimization, fluid flow analysis, decisions regarding whether additional features are included to provide receiver internal structural support, and manufacturing considerations.

The aspects of an elliptical receiver, internal tube, and internal structure are optionally applied either individually or together. These aspects achieve the benefits of reducing salt held in the receiver, which would in turn cause (a) reduced receiver sag, (b) reduced fluid cost, and (c) reduced fluid loop transit times. In addition, the elliptical receiver surface area is also decreased, causing (d) reduced thermal radiation loss and (e) reduced receiver cost. Reducing cross-sectional fluid area also achieves the benefit of reducing the required header section area, causing (f) reduced header pipe cost and (g) further reductions in fluid cost.

Example 2 Solar Receivers with Reduced Circumferential Temperature Distribution

Traditional Construction. The traditional construction of the receiver tube has an absorber tube nested within a glass envelope. The heat transfer fluid (HTF) flows though the absorber tube, and a vacuum is maintained between the glass envelope and the absorber tube. This construction is shown in FIG. 3.

Alternative Construction. The alternative construction described in this Example uses a second smaller tube inserted within the absorber tube to produce an annulus cross section for the HTF to pass through. The HTF does not flow through the inner tube. The inner tube optionally allows for the flow of a secondary fluid within it, though in some embodiments, no secondary fluid flows within the inner tube. One alternative construction embodiment is shown in FIG. 4.

Circumferential Temperature Distribution. The alternative cross-sectional area (Area 2 in FIG. 4) is smaller area than the traditional construction (Area 1 in FIG. 3). For the same mass or volumetric flow rates at the same operating temperatures, the velocity of the flow in the annulus of the alternative construction described in this Example is faster since it is passing the same quantity (mass/volume) of HTF through a smaller area. The faster fluid velocity increases the convective heat transfer from the absorber tube wall to the HTF.

Due to the optics of certain parabolic trough collector embodiments, the focused light only illuminates one side of the receiver. Since the receiver is not uniformly illuminated, the illuminated side is significantly hotter than the non-illuminated side. This creates a non-uniform circumferential temperature distribution on the absorber tube. The increased convective heat transfer reduces the temperature difference between the illuminated and the non-illuminated sides of the receiver.

The non-uniform circumferential temperature distribution also causes bowing in the absorber tube since the tube material does not expand uniformly. This bowing can be significant enough to cause absorber tube failure. By reducing the temperature difference between the illuminated and non-illuminated sides of the receiver, the bowing in the receiver is reduced.

Modeling results describing the relationship between the HTF velocity and the resulting circumferential temperature distribution and the bowing and stresses associated with the circumferential temperature distribution are described below in Example 4 and can also be found in the paper “Modeling and Analysis of Stress in High Temperature Molten Salt Trough Receivers”, SolarPACES 2013, Energy Procedia (in press), which is hereby incorporated by reference in its entirety.

Freeze Recovery. Some applications of receiver tube utilize an HTF that has the potential to freeze in the absorber tube if the operating temperature falls below the freezing point. The inner tube can facilitate freeze recovery by flowing a heated fluid through the inner tube to thaw the frozen HTF.

Inner Tube Collapsible Geometries. Most HTFs used in the absorber tube will contract when freezing. When the HTF is thawed, the fluid will expand. If there is not space for the HTF to expand into, the absorber tube will rupture due to the extreme pressures that result. To allow for the expansion, the inner tube can be manufactured with a collapsible geometry that allows for the volume in the annulus to expand as needed. The collapsible geometry optionally includes features such as convolutions and/or diaphragms.

Reduction in Salt Volume. Since the inner tube reduces the cross-sectional area that the HTF flows through, the total volume of HTF in the receiver is reduced. This becomes significant when molten salt is used since it is denser than other HTFs. The weight of the HTF is supported by the absorber tube and causes the tube to bow. The bowing causes a portion of the absorber tube to move out of focus. This reduces performance. By minimizing bowing, performance can be maintained.

Suspension. In embodiments, the inner tube is concentric with the absorber tube. To achieve this, some form of suspension is needed to position the inner tube. One option is a 5-pointed spring. Each leg of the spring comprises two thin elements that meet at a point on the inside wall of the absorber tube. The legs are attached to the inner tube. The legs can flex so that legs make intimate contact with the absorber wall, and the flexure also allows the inner tube to be installed into the absorber tube. This option is shown in FIG. 5.

Another option is to use a 3 leg spider to position the inner tube. The spider is attached to the inner tube and the legs are rigid. This option is shown in FIG. 6. To facilitate the insertion of the inner tube into the absorber tube, the legs are optionally manufactured so that a gap exists between the ends and the inner wall of the absorber tube.

Example 3 Solar Receivers Featuring Nested Inner Tubes

Nesting and Joining. In this example, the nesting of the inner tube is provided so that the inner tube is concentric with the absorber. This nesting is shown in FIG. 7.

If adjacent inner tubes need to be joined, the ends of the inner tube can be slid out past the edge of the absorber tube to provide access to the joint for welding. Once welding is completed, the adjacent absorber tubes can be slid together and welded. This is shown in FIG. 8.

Alternately, if the inner tubes do not need to be joined, the ends of each individual inner tube will be capped. The cap prevents the HTF from flowing through the inner tube. The caps are shown in FIG. 9. If the inner tube will be used to pass an electric current for impedance heating, a bridge will be installed to electrically connect adjacent inner tubes. The bridge is shown in FIG. 10.

End of Solar Collector Assembly Joint. If the inner tubes along the Solar Collector Assembly (SCA) are connected as shown in FIG. 7, at the end of the SCA, the inner tube must pass through the absorber tube. The absorber tube at the end of the SCA is fitted with an elbow. The elbow has a hole so that a straight section of the inner tube can pass through. This configuration is shown in FIG. 11.

Flow Turbulators. The inner tube is optionally fitted with features to induce turbulent flow of the HTF. One possibility is using cylindrical pins that are perpendicular to the axis of the inner tube and perpendicular to the flow of the HTF. The turbulent flow will improve the heat transfer from the absorber wall into the HTF. As a result, the circumferential temperature distribution will be reduced. The turbulators are shown in FIG. 12.

Example 4 Modeling and Analysis of Stress in High Temperature Molten Salt Trough Receivers

This example investigates the stresses and deformations occurring in parabolic trough receivers operating at temperatures above 425° C. Operating at these temperatures allows for direct molten salt storage and higher efficiency conversion from thermal to electric energy. However, at these temperatures, the typical stainless steels used in receiver construction are susceptible to chromium carbide precipitation. After the precipitation has occurred, the steel is vulnerable to intergranular corrosion, and the fatigue strength of the steel is reduced. Corrosion increases the stresses in the receiver walls, and the reduced fatigue strength lowers the stress limit where failure will occur. This example describes the results of an analysis of these stresses and an evaluation of the receiver material at these operating temperatures. This example shows that parabolic trough receivers can be designed to mitigate the negative effects of chromium carbide precipitation and operate above 425° C. without risk of premature failure.

Introduction and Background. Molten salt operation allows Concentrating Solar Power (CSP) parabolic troughs to operate at higher operating temperatures, and facilitates direct molten salt storage. The service life of the receivers at higher temperatures has been investigated in this analysis. For the operating conditions described here, the analysis indicates that a receiver has an adequate service life.

The primary steel alloys used in the thermal receivers of parabolic troughs are AISI 300 series stainless steels. This series of stainless steel exhibits good corrosion resistance and strength at elevated temperatures. The alloying element that gives the steel its corrosion resistance is chromium. As long as the concentration of chromium does not drop below 12%, the steel will remain resistant to corrosion. Between 425° C. and 870° C., the chromium precipitates into the grain boundary of the stainless steel as chromium carbide. Chromium carbide precipitation depletes the material near the grain boundary of chromium. This makes the stainless steel sensitive to intergranular corrosion. Intergranular corrosion will, over time, reduce the receiver wall thickness, thereby increasing the localized stress from operating loads. Operating between 425° C. and 870° C. also reduces the fatigue strength of the stainless steel.

Operating stress is caused by the pressure of the molten salt and uneven heating of the receiver. The stress from the pressure is well understood, but the stress from uneven heating is more difficult to quantify. The receiver is subjected to higher concentration of flux on the portion facing the trough than the portion facing away. The portion of the receiver with the higher flux is at a higher temperature, and expands more than the portion facing away. The uneven expansion causes bowing and high point stresses where the bowing is resisted near the receiver supports.

To assess the resulting stresses from uneven heating, a three part analysis was performed. First, the flux distribution on the receiver was determined. From the flux distribution, the resulting temperature distribution was derived from known heat transfer behavior. The resulting temperature distribution was then incorporated into a receiver Finite Element Analysis (FEA) to determine the stresses on the receiver. The reference coordinate systems for the analysis are shown in FIG. 13, which depicts the trough 3-dimensional coordinate system, and FIG. 14, which depicts the receiver angular position coordinate system.

The molten salt used in the modelling is a solar binary salt with 60% NaNO₃ and 40% KNO₃. The properties of this salt can be found in Solar Power Tower Design Basis Document, Zavoico, A. B., SAND2001-2100, Albuquerque, N. Mex.: Sandia National Laboratories, 2001.

Nomenclature: r, Radius on Receiver; φ, Angular location on receiver; k, Thermal conductivity; {dot over (q)} Heat absorbed by control volume; {dot over (q)}_(r), Flux along r; {dot over (q)}_(φ), Flux along φ.

Flux on the Receiver. The flux on the receiver can be determined from using either a ray trace program or an analytical method. Some ray tracing programs that are available include SolTrace and ASAP. For this example, an analytical model was constructed and compared to SolTrace results. The model assumed that the optical error can be characterized by a Gaussian distribution with a standard deviation of 5 mrad. Sun shape was also included and was based on published profiles. The rim angle of the collector was fixed at 82.5° and the concentration ratio was varied from 60 to 120. The resulting flux distribution is shown in FIG. 15, which provides the unit flux distribution on the receiver at different concentration ratios.

The flux shown is normalized so that the total flux on the receiver, i.e. the area under the curve, is equal to 1 m⁻² to allow adjustment of the distribution for any trough aperture width and Direct Normal Insolation (DNI).

Receiver Temperature Distribution. Once the flux is determined, the circumferential temperature distribution of the receiver wall can be established. Some previous modelling efforts have only considered the temperature distribution along the length of the receiver, but not circumferential. To determine the circumferential distribution, a finite difference model was developed. The model is based on the Heat Equation in cylindrical coordinates:

${{\frac{1}{r}\frac{\partial}{\partial r}\left( {{kr}\frac{\partial T}{\partial r}} \right)} + {\frac{1}{r^{2}}\frac{\partial}{\partial\varphi}\left( {k\frac{\partial T}{\partial\varphi}} \right)} + {\frac{\partial}{\partial z}\left( {k\frac{\partial T}{\partial z}} \right)} + \overset{.}{q}} = {\rho \; c_{p}{\frac{\partial T}{\partial t}.}}$

The model is simplified by assuming that heat transfer in the z direction (along the axis of the receiver) is insignificant. Based on this assumption, the heat transfer in the z direction is set to zero and the equation reduces to the following:

${{\frac{1}{r}\frac{\partial}{\partial r}\left( {{kr}\frac{\partial T}{\partial r}} \right)} + {\frac{1}{r^{2}}\frac{\partial}{\partial\varphi}\left( {k\frac{\partial T}{\partial\varphi}} \right)} + \overset{.}{q}} = {\rho \; c_{p}\frac{\partial T}{\partial t}}$ where: ${{\overset{.}{q}}_{r} = {{{- k}\frac{\partial T}{\partial r}\mspace{31mu} {\overset{.}{q}}_{\varphi}} = {{- \frac{k}{r}}\frac{\partial T}{\partial\varphi}}}},$

and where the differential control volume is shown in FIG. 16.

Convection occurs between the molten salt and the receiver's inner wall. Between the inner and outer receiver walls, heat transfer is in the form of conduction. The heat transfer between the outer receiver wall and the glass envelope is modelled as radiation. A high vacuum exists between the receiver and glass envelope; consequently, conduction and convection are neglected. Finally, both conduction and convection occur between the glass envelope and the surrounding air.

The model performs iterative calculations until the temperature change in all of the differential control volumes becomes zero. The circumferential temperature distribution is a function of flow rate, molten salt temperature, and Direct Normal Insolation (DNI). FIGS. 17A and 17B show temperature distribution along the outer surface of the receiver at peak insolation levels in a trough with a concentration ratio of 80/π, with various flow rates and molten salt temperatures shown. Specifically, FIG. 17A shows receiver wall temperature as a function of molten salt flow rate for DNI=1000 W/m², Receiver Outer Diameter=90 mm, Concentration Ratio=80/π, and Fluid Temperature=500° C.; and FIG. 17B shows receiver wall temperature difference (from wall minimum temperature) as a function of molten salt temperature with DNI=1000 W/m², Receiver Outer Diameter=90 mm, Concentration Ratio=80/π, and Flow Rate=8 kg/s. While lower fluid temperatures produce slightly larger temperature differences around the circumference, the mean wall temperature is higher with higher temperature molten salt. The strength of stainless steel decreases at higher temperatures; consequently, the model results in this example are presented for the higher temperature molten salt. The magnitude of the displacement, or bow, of the receiver is proportional to the difference between the maximum and minimum temperatures. This difference increases as the flow rate reduces. This is shown in FIG. 18 for several concentration ratios, which provides receiver wall circumferential temperature difference as a function of flow rate for four concentration ratios.

As described below, the magnitude of the stress and strain is proportional to the difference between the maximum and minimum temperatures around the circumference of the receiver. This difference increases as the flow rate decreases. This is shown in FIG. 18 for several concentration ratios.

Receiver FEA Model. SolidWorks Simulation is used to perform the Finite Element Analysis (FEA) to model stress in the receiver. The receiver is modelled as a circular tube with the wall represented as a 2 dimensional shell. The trough receiver supports are included in the model to provide the mechanical boundary constraints, and do not allow rotation at the supports. One support does not allow translation, while the second allows translation only along the receiver axis. This translation accommodates the net thermal expansion that occurs as the receiver average temperature rises from ambient to working temperature. The receiver and a trough receiver support are shown in FIG. 19A. FIG. 19A also shows the location of the peak stress in the receiver.

FIG. 19B shows that the maximum stress has a linear relation to the temperature difference between the hot and cold sides of the receiver. The strain is also of interest. FIG. 20 shows the maximum strain the receivers withstand as a function of the receiver wall temperature difference for four receiver wall thicknesses.

Receiver Service Life. The primary material used to make the absorber element of the receiver is AISI 300 series stainless steel. This series of steel is selected for its corrosion resistance and relatively low cost. At temperatures between 425° C. and 870° C., the 300 series material will undergo chromium carbide precipitation. Precipitation can be minimized by reducing the concentration of carbon in the steel as in AISI 316L (UNS S31603) stainless steel. As an alternative, additional alloying elements can be added that will form other carbides (instead of chromium carbide). Titanium is used for this purpose in AISI 316Ti (UNS S31635) stainless steel and AISI 321 (UNS S32100) stainless steel.

Studies have been performed to evaluate the rate of corrosion of various 300 series stainless steels. The corrosion rate of AISI 321 stainless steel in a binary solar salt was 12.3 mg/cm²-yr. Extrapolating this rate out to 30 years, the receiver wall will thin by 0.5 mm. A second study found the corrosion rate for AISI 316 stainless steel in binary salt to be 10.2 mg/cm²-yr. Again, extrapolating this out to 30 years, the receiver wall thickness will be reduced by 0.4 mm. The reduction in thickness will increase the stress in the receiver wall.

Chromium carbide precipitation also reduces the fatigue strength of 300 series stainless steel. The ASM handbook defines the allowable strain for AISI 316 stainless steel as 7×10⁻⁴ for 1,000,000 cycles at temperatures not exceeding 510° C. Combining this allowable strain with the results shown in FIG. 20 gives the maximum receiver wall temperature difference during normal operating conditions for a given wall thickness. This result is shown in FIG. 21.

A generalized collector loop was used to evaluate whether normal operating conditions will cause the receiver to fail. The following parameters were used: Receiver Dimensions=90 mm Outer Diameter×3 mm Wall thickness×4.7 m length; Fluid Outlet Temperature=500° C.; Service Life=30 Year; Receiver Material=AISI 316 Stainless Steel; Collector Thermal Efficiency=70%; DNI=1000 W/m²; Binary Solar Salt; Number of Solar Collector Arrays (SCA) per Loop=6 SCA's; Number of Receivers per SCA=24 Receivers.

The above parameters were also used to determine the required flow rate to maintain a given inlet temperature and outlet temperature. These results are shown in FIG. 22A. The flow rates were then used to determine the circumferential temperature difference using the relations shown in FIG. 18. Strain was then calculated from FIG. 20 based on the temperature differences. The results are shown in FIG. 22B. The calculated strains are below the 7×10⁻⁴ maximum given in Elevated-Temperature Properties of Stainless Steels.

The number of Solar Collector Arrays per loop was then reduced to one, to illustrate the impact of a very large temperature increase as molten salt passes through each receiver. These results are shown in FIG. 23. The maximum strain does exceed the 7×10⁻⁴ maximum for high concentration ratios and temperature rises per receiver.

A 90 mm diameter receiver with a wall thickness of 3 mm will provide a service life in excess of 30 years on parabolic troughs with a concentration ratio of 80/π, a temperature rise per receiver of less than 10° C., and a molten salt temperature that does not exceed 510° C.

Additional analysis is required to verify the adequacy of receivers for special operating conditions. For example, during fill, the molten salt creates circumferential temperature differences. This impact could be substantially reduced with receiver preheat, particularly if the difference between salt and wall temperatures are less than 50° C. The freezing and thawing of salt in receivers can also exert extremely high stresses that can rupture the receivers. These pressures were not evaluated in this analysis.

The analysis indicates that AISI 300 series molten salt receivers operating at high temperatures as described here, have an adequate service life.

Example 5 Heat Transfer Coefficient Relations

This example describes the relations between various properties, characteristics, geometries, and dimensions governing the flow of a heat transfer fluid (HTF) in a linear concentrating solar thermal collection system.

The mass flow rate {dot over (m)} and volumetric flow rate V have the following relationship:

{dot over (m)}∝ V   (1)

Volumetric flow rate and fluid velocity have the following relation:

$\begin{matrix} {\overset{\_}{V} = \frac{V}{A}} & (2) \end{matrix}$

where, V=HTF velocity A=Flow cross section Substituting this relation into the mass flow relation yields:

$\begin{matrix} {\overset{.}{m} \propto \frac{V}{A}} & (3) \end{matrix}$

This relation shows that for the same mass flow rate, the annular flow in a linear receiver including a volume displacement will have a faster fluid velocity, since it has a smaller area, than the linear receiver without the volume displacement. The pumping losses are proportional to the fluid velocity. This means the annular flow will have proportionally higher pumping losses for the same flow rate.

For reasonable flow rates, the flow will always be turbulent. Therefore, the following relationship can be used between the Nusselt number (Nu) and the Reynolds Number:

Nu∝Re ^(0.8)  (4)

The Reynolds number is given by:

$\begin{matrix} {{Re} = \frac{\rho \; {VD}}{\mu}} & (5) \end{matrix}$

where, ρ=HTF density D=characteristic dimesion of the flow μ=HTF dynamic viscosity

The Nusselt number is given by:

$\begin{matrix} {{Nu} = \frac{hD}{k}} & (6) \end{matrix}$

where, h=HTF convective heat transfer coefficient k=HTF thermal conductivity This makes the relationship the following:

$\begin{matrix} {\frac{hD}{k} \propto {k\left( \frac{\rho \; {VD}}{\mu} \right)}^{0.8}} & (7) \end{matrix}$

The relationship can be rearranged to the following:

$\begin{matrix} {h \propto \frac{{k\left( \frac{\rho \; {VD}}{\mu} \right)}^{0.8}}{D}} & (8) \end{matrix}$

Given a mass flow rate, the velocity has the following relationship:

$\begin{matrix} {V \propto \frac{k}{D_{1}^{2} - D_{2}^{2}}} & (9) \end{matrix}$

where, D₁=Diameter of receiver tube D₂=Diameter of inner tube

The characteristic dimension for the flow is given by the following relation:

D=D ₁ −D ₂  (10)

Substituting these relations into our function yields:

$\begin{matrix} {h \propto \frac{{k\left( {\frac{\rho \; k}{\mu}\frac{D_{1} - D_{2}}{D_{1}^{2} - D_{2}^{2}}} \right)}^{0.8}}{D_{1} - D_{2}}} & (11) \end{matrix}$

For this analysis, the fluid properties can be assumed to be constant and therefore:

$\begin{matrix} {h \propto \frac{\left( \frac{1}{D_{1}^{2} - D_{2}^{2}} \right)^{0.8}}{\left( {D_{1} - D_{2}} \right)^{0.2}}} & (12) \end{matrix}$

REFERENCES

-   U.S. Patent Application Publication Nos. 2009/0293866, 2013/0220310,     2013/0276775, 2013/0319501. -   Black, J. T., Ronald A. Kohser, and E. Paul DeGarmo. DeGarmo's     Materials and Processes in Manufacturing. Hoboken, N.J.: Wiley,     2008. -   Breault Research Organization. ASAP. n.d.     http://www.breault.com/software/asap.php (accessed May 17, 2013). -   Elevated-Temperature Properties of Stainless Steels. Vol. 1, in     Properties and Selection: Irons, Steels, and High Performance     Alloys, p. 930-949. ASM International, 1990. -   Forristall, R. Heat Transfer Analysis and Modeling of a Parabolic     Trough Solar Receiver Implemented in Engineering Equation Solver.     Technical Report, Golden, Colo.: National Renewable Energy     Laboratory, 2003. -   Goods, S. H., R. W. Bradshaw, M. R. Prairie, and J. M. Chavez.     Corrosion of Stainless and Carbon Steels in Molten Mixtures of     Industrial Nitrates. Rep. no. SAND94-8211, Albuquerque, N. Mex.:     Sandia National Laboratories, 1994. -   High Temperature Characteristics of Stainless Steels. A Designers'     Handbook Series No. 9004, American Iron and Steel Institute, 2011. -   Incropera, Frank P., David P. DeWit. Introduction to Heat Transfer.     New York: Wiley, 1996. -   Kruizenga, A. M., and D. D. Gill. “Material Performance of Alloys in     NaNO3/KNO3 at 6000.” ECS. Honolulu, Hi.: SAND2012-8621P, 2012. -   National Renewable Energy Labratory. SolTrace Optical Modelling     Software. n.d. http://www.nrel.gov/csp/soltrace/(accessed May 17,     2013). -   Rabl, Ari. Active Solar Collectors and Their Application. New York:     Oxford University Press, 1985. -   Zavoico, A. B. Solar Power Tower Design Basis Document.     SAND2001-2100, Albuquerque, N. Mex.: Sandia National Laboratories,     2001. -   http://www.schott.com/csp/media/img/csp-receiver.jpg, retrieved Dec.     30, 2013. -   http://www.us.schott.com/csp/english/schott-solar-ptr-70-receivers.html,     retrieved Dec. 30, 2013.

STATEMENTS REGARDING INCORPORATION BY REFERENCE AND VARIATIONS

All references throughout this application, for example patent documents including issued or granted patents or equivalents; patent application publications; and non-patent literature documents or other source material; are hereby incorporated by reference herein in their entireties, as though individually incorporated by reference, to the extent each reference is at least partially not inconsistent with the disclosure in this application (for example, a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference).

All patents and publications mentioned in the specification are indicative of the levels of skill of those skilled in the art to which the invention pertains. References cited herein are incorporated by reference herein in their entirety to indicate the state of the art, in some cases as of their filing date, and it is intended that this information can be employed herein, if needed, to exclude (for example, to disclaim) specific embodiments that are in the prior art. For example, when a compound is claimed, it should be understood that compounds known in the prior art, including certain compounds disclosed in the references disclosed herein (particularly in referenced patent documents), are not intended to be included in the claim.

When a group of substituents is disclosed herein, it is understood that all individual members of those groups and all subgroups and classes that can be formed using the substituents are disclosed separately. When a Markush group or other grouping is used herein, all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure. As used herein, “and/or” means that one, all, or any combination of items in a list separated by “and/or” are included in the list; for example “1, 2 and/or 3” is equivalent to “‘1’ or ‘2’ or ‘3’ or ‘1 and 2’ or 1 and 3′ or ‘2 and 3’ or ‘1, 2 and 3’”.

Every formulation or combination of components described or exemplified can be used to practice the invention, unless otherwise stated. Specific names of materials are intended to be exemplary, as it is known that one of ordinary skill in the art can name the same material differently. One of ordinary skill in the art will appreciate that methods, device elements, starting materials, and synthetic methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation. All art-known functional equivalents, of any such methods, device elements, starting materials, and synthetic methods are intended to be included in this invention. Whenever a range is given in the specification, for example, a temperature range, a time range, or a composition range, all intermediate ranges and subranges, as well as all individual values included in the ranges given are intended to be included in the disclosure.

As used herein, “comprising” is synonymous with “including,” “containing,” or “characterized by,” and is inclusive or open-ended and does not exclude additional, unrecited elements or method steps. As used herein, “consisting of” excludes any element, step, or ingredient not specified in the claim element. As used herein, “consisting essentially of” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim. Any recitation herein of the term “comprising”, particularly in a description of components of a composition or in a description of elements of a device, is understood to encompass those compositions and methods consisting essentially of and consisting of the recited components or elements. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations which is not specifically disclosed herein.

The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims. 

We claim:
 1. A linear receiver for a concentrating solar collector, said receiver comprising: a linear solar radiation absorbing element extending along a first length, wherein said linear solar radiation absorbing element comprises a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; a linear volume displacement element positioned within said linear solar radiation absorbing element and extending along at least a portion of said first length of said linear solar radiation absorbing element, wherein said first internal volume includes a second volume occupied by said linear volume displacement element and a third volume not occupied by said linear volume displacement element and wherein said second volume occupies a percentage of said first internal volume greater than 15%; and a first heat transfer fluid provided within said third volume of said linear solar radiation absorbing element, wherein said first heat transfer fluid flows at a first flow rate within said linear solar radiation absorbing element and does not flow within said second volume.
 2. The linear receiver of claim 1, wherein said second volume occupies a percentage of said first internal volume selected from the range of 15% to 90%.
 3. The linear receiver of claim 1, wherein said linear volume displacement element extends along a percentage of said first length selected from the range of 50% to 100%.
 4. The linear receiver of claim 1, wherein said linear volume displacement element comprises a solid structure or a hollow structure.
 5. The linear receiver of claim 1, wherein said linear volume displacement element comprises an electrically conductive material.
 6. The linear receiver of claim 1, wherein said linear volume displacement element has a cross-sectional shape selected from the group consisting of a circle, an oval, an ellipse, a rectangle and a square.
 7. The linear receiver of claim 1, wherein said linear volume displacement element is positioned concentrically within said linear solar radiation absorbing element.
 8. The linear receiver of claim 1, wherein said linear volume displacement element comprises two or more linear volume displacement elements.
 9. The linear receiver of claim 1, wherein said linear volume displacement element has an overall density less than a density of said first heat transfer fluid.
 10. The linear receiver of claim 1, wherein said linear volume displacement element comprises a cylindrical tube or a solid structure.
 11. The linear receiver of claim 1, wherein said linear volume displacement element comprises a second hollow structure.
 12. The linear receiver of claim 11, wherein said second hollow structure has a wall thickness that is a percentage of a diameter of said second hollow structure selected from the range of 1% to 40%.
 13. The linear receiver of claim 11, further comprising a second heat transfer fluid provided within said second hollow structure.
 14. The linear receiver of claim 1, wherein said linear volume displacement element comprises a collapsible geometry.
 15. The linear receiver of claim 1, wherein said linear solar radiation absorbing element comprises a cylindrical tube.
 16. The linear receiver of claim 1, wherein said linear solar radiation absorbing element has a cross-sectional shape selected from the group consisting of a circle, an oval, an ellipse, a rectangle and a square.
 17. The linear receiver of claim 1, further comprising one or more turbulators positioned within said third volume.
 18. The linear receiver of claim 1, further comprising a hollow glass structure, wherein said linear solar radiation absorbing element is positioned within said hollow glass structure.
 19. A solar collector comprising the linear receiver of claim
 1. 20. The solar collector of claim 19, wherein said solar collector comprises a linear concentrating solar collector, a reflective parabolic trough solar collector or a reflective linear Fresnel solar collector positioned to reflect incident solar radiation onto said linear receiver.
 21. A method of collecting concentrated solar radiation, the method comprising steps of: providing a linear solar radiation absorbing element extending along a first length, wherein said linear solar radiation absorbing element comprises a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; providing a linear volume displacement element within said linear solar radiation absorbing element and extending along at least a portion of the first length of said linear solar radiation absorbing element, wherein said first internal volume includes a second volume occupied by said linear volume displacement element and a third volume not occupied by said linear volume displacement element and wherein said second volume occupies a percentage of said first internal volume greater than 15%; and flowing a first heat transfer fluid within said third volume of said linear solar radiation absorbing element, wherein said first heat transfer fluid flows at a first flow rate within said linear solar radiation absorbing element and does not flow within said second volume; and exposing said linear solar radiation absorbing element to concentrated solar radiation, wherein said first flow rate is sufficient to maintain a maximum circumferential temperature difference of the linear solar radiation absorbing element to achieve a target amount of bowing, stress and/or strain in the linear solar radiation absorbing element.
 22. A method of making a concentrating solar collector, the method comprising steps of: providing a linear solar radiation absorbing element extending along a first length, wherein said linear solar radiation absorbing element comprises a hollow structure having a first internal volume and an external surface for absorbing incident or reflected solar radiation; providing a linear volume displacement element within said linear solar radiation absorbing element and extending along at least a portion of said first length of said linear solar radiation absorbing element, wherein said first internal volume includes a second volume occupied by said linear volume displacement element and a third volume not occupied by said linear volume displacement element and wherein said second volume occupies a percentage of said first internal volume greater than 15%; flowing a first heat transfer fluid at a first flow rate within said third volume and between an internal surface of said linear solar radiation absorbing element and said linear volume displacement element, wherein said first heat transfer fluid does not flow within said second volume; and positioning said linear receiver at a location to receive concentrated solar radiation from one or more reflective surfaces.
 23. The method of claim 22, wherein said one or more reflective surfaces comprise one or more parabolic trough mirrors or one or more mirrors of a linear Fresnel solar collector. 